Robustness of Quantum Markov Chains

B Ibinson, N Linden, AJ Winter

Research output: Contribution to journalArticle (Academic Journal)peer-review

59 Citations (Scopus)


If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.
Translated title of the contributionRobustness of Quantum Markov Chains
Original languageEnglish
Pages (from-to)289 - 304
Number of pages16
JournalCommunications in Mathematical Physics
Volume277, number 2
Publication statusPublished - Jan 2008

Bibliographical note

Publisher: MetaPress


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